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A note on oscillating neutrino states in quantum field theory
No full textIn a recent paper [Eur. Phys. J. C80, 68 (2020)], a definition of oscillating neutrino states in quantum field theory was proposed. We show that such definition can be derived as a particular case of the Blasone–Vitiello approach, when mass vacuum is chosen as the physical vacuum. We discuss some problems of such an approach, which appears to be mathematically inconsistent and physically not acceptable
Ordering kinetics of the two-dimensional voter model with long-range interactions
Full text linkWe study analytically the ordering kinetics of the two-dimensional long-range voter model on a two-dimensional lattice, where agents on each vertex take the opinion of others at distance r with probability P(r)∝ r-α. The model is characterized by different regimes, as α is varied. For α>4, the behavior is similar to that of the nearest-neighbor model, with the formation of ordered domains of a typical size growing as L(t) ∝ t, until consensus is reached in a time of the order of NlnN, with N being the number of agents. Dynamical scaling is violated due to an excess of interfacial sites whose density decays as slowly as ρ(t) ∝ 1/lnt. Sizable finite-time corrections are also present, which are absent in the case of nearest-neighbor interactions. For 0<α≤4, standard scaling is reinstated and the correlation length increases algebraically as L(t) ∝ t1/z, with 1/z=2/α for 3<α<4 and 1/z=2/3 for 0<α<3. In addition, for α≤3, L(t) depends on N at any time t>0. Such coarsening, however, only leads the system to a partially ordered metastable state where correlations decay algebraically with distance, and whose lifetime diverges in the N→∞ limit. In finite systems, consensus is reached in a time of the order of N for any α<4
Neutrino mixing, entanglement and the gauge paradigm in quantum field theory
Full text linkWe shortly review the quantum field theory formulation of neutrino mixing and oscillations extensively studied in literature. The canonical formalism requires a non-trivial condensate structure of the flavor vacuum, which appears to be an entangled coherent state. Within such a frame, mixing is described as resulting from the interaction of the neutrino field with a non-abelian gauge field
Time–Energy Uncertainty Relation for Neutrino Oscillations: Historical Development, Applications, and Future Prospects
No full textThe time–energy uncertainty relation (TEUR) plays a fundamental role in quantum mechanics, as it allows the grasping of peculiar aspects of a variety of phenomena based on very general principles and symmetries of the theory. Using the Mandelstam–Tamm method, TEUR has recently been derived for neutrino oscillations by connecting the uncertainty in neutrino energy with the characteristic timescale of oscillations. Interestingly, the suggested interpretation of neutrinos as unstable-like particles has proved to naturally emerge in this context. Further aspects were later discussed in semiclassical gravity theory, by computing corrections to the neutrino energy uncertainty in a generic stationary curved spacetime, and in quantum field theory, where the clock observable turns out to be identified with the non-conserved flavor charge operator. In the present work, we give an overview on the above achievements. In particular, we analyze the implications of TEUR and explore the impact of gravitational and non-relativistic effects on the standard condition for neutrino oscillations
Generalized generating functional for mixed-representation Green's functions: A quantum-mechanical approach
No full textWhen one tries to take into account the nontrivial vacuum structure of quantum field theory, the standard functional-integral tools, such as generating functionals or transitional amplitudes, are often quite inadequate for such purposes. Here we propose a generalized generating functional for Green's functions which allows one to easily distinguish among a continuous set of vacua that are mutually connected via unitary canonical transformations. In order to keep our discussion as simple as possible, we limit ourselves to quantum mechanics where the generating functional of Green's functions is constructed by means of phase-space path integrals. The quantum-mechanical setting allows us to accentuate the main logical steps involved without embarking on technical complications such as renormalization or inequivalent representations that should otherwise be addressed in the full-fledged quantum field theory. We illustrate the inner workings of the generating functional obtained by discussing Green's functions among vacua that are mutually connected via translations and dilatations. Salient issues, including connection with quantum field theory, vacuum-to-vacuum transition amplitudes, and perturbation expansion in the vacuum parameter, are also briefly discussed
Effective action approach to dynamical generation of fermion mixing
Full text linkIn this paper we discuss a mechanism for the dynamical generation of flavor mixing, in the framework of the Nambu-Jona Lasinio model. Our approach is illustrated both with the conventional operatorial formalism and with functional integral and ensuing one-loop effective action. The results obtained are briefly discussed
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